A234253 a(n) = Sum_{i=1..n} C(7+i,8)^2.

1, 82, 2107, 29332, 274357, 1930726, 10948735, 52357960, 217994860, 808970960, 2723733524, 8436372248, 24304813148, 65712993248, 167965846148, 408373664744, 949291256585, 2119095737210, 4559798912835, 9488531918460, 19148848609485, 37571357310510

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 13.

Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).

Formula

G.f.: x*(x^8 +64*x^7 +784*x^6 +3136*x^5 +4900*x^4 +3136*x^3 +784*x^2 +64*x +1) / (x-1)^18. - Colin Barker, May 02 2014

Maple

A234253:=n->add(binomial(7+i, 8)^2, i=1..n); seq(A234253(n), n=1..30); # Wesley Ivan Hurt, Dec 23 2013

Mathematica

Table[Sum[Binomial[7 + i, 8]^2, {i, n}], {n, 30}] (* Wesley Ivan Hurt, Dec 23 2013 *)
CoefficientList[Series[(x^8 + 64 x^7 + 784 x^6 + 3136 x^5 + 4900 x^4 + 3136 x^3 + 784 x^2 + 64 x + 1)/(x - 1)^18, {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2014 *)

Prog

(PARI) Vec(x*(x^8 +64*x^7 +784*x^6 +3136*x^5 +4900*x^4 +3136*x^3 +784*x^2 +64*x +1)/(x-1)^18 + O(x^100)) \\ Colin Barker, May 02 2014

Crossrefs

Cf. A087127, A086023, A086025, A086027, A086029.

Sequence in context: A282155 A280857 A281603 * A031606 A232904 A230395

Adjacent sequences: A234250 A234251 A234252 * A234254 A234255 A234256

Keyword

nonn,easy

Author

Yahia Kahloune, Dec 22 2013

Extensions

One term corrected and more terms from Colin Barker, May 02 2014

Status

approved